Discrete Random Variables

A variable is represented by a capital letter i.e. X

This can be any particular x valueA discrete random variable can only be certain discrete valuesP(X = x) is the probability that the random variable is the same as a particular value of xYou will be given P(X = x) in an exam

Probability Distribution

A probability distribution is a table like above

REMEMBERthat it's probability, soΣP(X=x) = 1

What if:

Here there are two different probabilities and a constant

So k + 3k + (2-1)k + (4-1)k = 1 8k = 1 k = 1/8

What if:

P(1 < X < 5)

This is the same as P(X = 2,3 or 4)

P(X = 2) = 0.2P(X = 3) = 0.3P(X = 4) = 0.25

P(1 < X < 5) = 0.75

Cumulative Distribution Function

Mean / Expected Value and Variance

This gives the mean of the data

E(X) = ΣxP(X=x)

Using this formula means to multiply each P(X = x) by the corresponding x value and find the sum of theseThis gives the mean of the data squared

Modeling

When you have a discrete uniform distribution, where the probability for every X value is the same, you can create a model which allows you to work out the mean and variance of X values up to an unknown amount (n)

So when x = 1,2,3... n

ThenP(X=x) = 1/n

For this

E(X) = n + 1 2

Var(X) = (n + 1)(n - 1)12

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Chubby Revision: A Level students revision for Chemistry, Physics, Geography and Maths